{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-simple-linear-time-algorithm-for-smallest","title":"A simple linear time algorithm for smallest enclosing circles on the (hemi)sphere","arxiv_id":"2407.19840","date":"2024-07-29","proceeding":null,"authors":["Jens Flemming"],"abstract":"Based on Welzl's algorithm for smallest circles and spheres we develop a simple linear time algorithm for finding the smallest circle enclosing a point cloud on a sphere. The algorithm yields correct results as long as the point cloud is contained in a hemisphere, but the hemisphere does not have to be known in advance and the algorithm automatically detects whether the hemisphere assumption is met. For the full-sphere case, that is, if the point cloud is not contained in a hemisphere, we provide hints on how to adapt existing linearithmic time algorithms for spherical Voronoi diagrams to find the smallest enclosing circle.","url_abs":"https://arxiv.org/abs/2407.19840v1","url_pdf":"https://arxiv.org/pdf/2407.19840v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-simple-linear-time-algorithm-for-smallest","repo_url":"https://github.com/jeflem/secots","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}